Consider the traffic flow diagram that follows, where a1, a2, a3, a4, b1, b2, b3, b4 are fixed posi-tive integers. Set up a linear system in the unknowns x1, x2, x3, x4 and show that the systemwill be consistent if and only ifa1 + a2 + az + a4 = b1 + b2 + b3 + b4What can you conclude about the number of automobiles entering and leaving the trafficnetwork?TH THb4X1X4A2X3b3Az

The complete solution is in given below

Answered: Consider the traffic flow diagram that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find 1) w(x,,x2,X3)for the system x, = tx,-2x2+3X3 x2= 5x, -3x2+X3 x3= - X2+ X3
Rewrite the system of inequalities, adding slack variables or subtracting surplus variables as necessary. 3x₁ + 4x₂ ≤ 8 X₁ + 4x₂ ≤ 7 Choose the new system. O A. 3x₁ + 4x2 + S₁ = 8, X₁ +4x₂+S₂ = 7 OB. 3x₁ +4x2+ S₁ = 8, X₁ + 4x₂-S₂ = 7 O C. 3x₁ +4x2 S₁ = 8, X₁ + 4x2-S₂ #7 O D. 3x1 +4x2 S₁ = 8, X₁ + 4x₂ + $₂ = 7
Determine whether the system is consistent: a) x1−x2+3x3=−11 −4x1+4x2−12x3=44 x1+3x2+x3=−17 −2x1+6x2−8x3=0 b) x1+2x2+x3=7 x1−x2+2x3=7 2x1+x2+3x3=14 5x1+x2+8x3=0
4. Consider the 2×2 linear system: a₁₁x₁ + a₁₂x²₂²₂ =b₁ a₂₁x²₁ + a₂₁x²₂ =b₂ Using an xy-Cartesian coordinate system, give a geometric interpretation of the possible solutions to this system.
For each system below that is linear, determine whether it is consistent. (a) (b) 5x₁ - x4 = 4 4x₁ + 4x₂ + x3 - 2x4 = -2 x1 + 2x₂ = x3 + 6x4
Suppose that in a biological system there are n species of animals and m sources of food. Let ï¿ represent the population of the jth species, for each j = 1, . . ., N; let bi represent the available daily supply of the ith food; and let aÿj represent the amount of the ith food consumed on average by a member of the jth species. The linear system a11x1 + a12X2 + + A1n xn b₁, a21x1 + a22x2 + + A2n xn : b2, am1x1 + am 2x2 + represents an equilibrium A. Let A = [aij] - = = ⠀ : bm + Amn Xn where there is a daily supply of food to precisely meet the average daily consumption of each species. = 1 2 0 3 = " 1 0 2 2 X = (xj) = [1000, 500, 350, 400], and b 0 0 1 1 (bį) = [3500, 2700, 900]. Is there sufficient food to satisfy the average daily consumption? (Hint: The linear system holds if Ax b. We don't exactly need this, but think about how the entries in Ax should be compared to those of b.) B. What is the maximum number of animals of species 1 that could be added to the system with the supply…
ao + a1x1 + Solve the following linear system ao + a1x0 + m-1 +am-1x0 + amxm m-1 = + am-1x1 + amxm = f(xo), f(x1), ... ... ... m-1 20 + 21x + + am-1xn + amxn = m f(xn), to obtain the interpolating polynomial Pm(x)=a0a1x+ m-1 + am-1xm + amxm Is the linear system above guaranteed to have a solution when m < n?
for system to be consistant, we must have k not equal to ?
6. Find the value(s) of h so that the linear system 6b) * xi +3x2 = -1 is inconsistent. 5x1 + hx2 =7
Three components are connected to form a system as shown in the accompanying diagram. Because the components in the 2–3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2–3 subsystem |-------2-------| ---1------>| |----------> |-------3-------| The experiment consists of determining the condition of each component [S(success) for a functioning component and F(failure) for a nonfunctioning component]. a. Which outcomes are contained in the event A that exactly two out of the three components function? b. Which outcomes are contained in the event B that at least two of the components function? c. Which outcomes are contained in the event C that the system functions? d. List outcomes in C', A U C, B U C.

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